ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
Unsigned basic expectation
Basic expectation
Random real number moment
Random real number central moment
Absolute central moment
Random real number variance
Definition D3844
Index of dispersion
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \mathbb{E} |X|^2 < \infty \end{equation}
(ii) \begin{equation} \mathbb{E} X \neq 0 \end{equation}
The index of dispersion of $X$ is the D993: Real number \begin{equation} \text{Disp} X : = \frac{\text{Var} X}{\mathbb{E} X} \end{equation}
Also known as
Variance-to-mean ratio, Variance-to-expectation ratio, Dispersion-to-location ratio
Children
D5276: Equidispersed random basic real number
D5277: Index of variation
D5274: Overdispersed random real number
D5275: Underdispered random real number